UAV autonomous swarm formation rotation control method based on simulated migratory bird evolutionary snowdrift game

ABSTRACT

A UAV autonomous swarm formation rotation control method based on a simulated migratory bird evolutionary snowdrift game includes steps of: Step 1: initializing; Step 2: determining flight mode based on a migratory bird evolutionary snowdrift game; Step 3: determining the leader and its position relative to corresponding wing UAV; Step 4: running UAV model; and Step 5: determining whether to end simulation. The present invention is to provide a distributed UAV autonomous swarm formation rotation control method, so as to improve robustness and adaptability of the UAV in autonomous swarm formation rotation, thus effectively improving long-range mission execution capability of the UAV.

CROSS REFERENCE OF RELATED APPLICATION

The present invention claims priority under 35 U.S.C. 119(a-d) to CN201810026713.3, filed Jan. 11, 2018.

BACKGROUND OF THE PRESENT INVENTION Field of Invention

The present invention relates to a UAV autonomous swarm formationrotation control method based on a simulated migratory bird evolutionarysnowdrift game, belonging to a technical field of UAV control.

Description of Related Arts

Unmanned Aerial Vehicle (UAV) is a powered aircraft that does not carryan operator, uses aerodynamics to provide lift, can fly autonomously orremotely, can be used once and can be recycled, and carries deadly ornon-fatal payloads. It has the basic attributes of “unmanned platformand manned system,” and has broad application prospects in military andcivilian fields.

The increased onboard capacity of the UAV has changed the missionexecution mode thereof. In the conventional mission execution mode, UAVstypically perform long-range missions by refueling in the air. In thechanged mission execution mode, the UAVs will perform long-distancetasks in the form of swarms, which are delivered and recycled by thehost. Since the host cannot reach the mission area under normalcircumstances for avoiding loss, the UAV swarm needs to have strongendurance. The formation of the UAV swarm enables the wing UAV in theswarm to effectively utilize the wake of the leader to reduce drag, savefuel, and extend range. However, the leading UAV of the swarm cannot usethe wake of any UAV, so its range is not extended. Therefore, the UAVswarm formation does not extend the overall range of the UAV swarm. Onlythrough UAV swarm formation rotation, which means the UAVs of the swarmtake turns to act as the leading UAV, can the overall range of the UAVswarm be effectively extended. That is to say, the design of areasonable and effective UAV autonomous swarm formation rotation controlmethod is vital. The present invention aims to improve the formationcontrol level of the UAV autonomous swarm by designing a UAV autonomousswarm formation rotation control method, so that the UAVs can performthe long-distance task with a lower fuel configuration.

Conventionally, the common method of UAV swarm rotation is mainlycyclical method, namely when a certain UAV in the swarm consumes theprescribed fuel as a leading UAV, UAVs in the swarm moves in a clockwiseor counterclockwise direction to act as a leading UAV the swarm in turn.Although this method is simple and easy, it has drawbacks as follows.Firstly, when a UAV in the UAV swarm fails, the method cannot continueto execute, so the robustness is poor. Secondly, the method is notapplicable to unconventional swarm formation except V formation andechelon formation. Besides, when the UAV fuel distribution in the UAVswarm is uneven, the method is not reasonable and the adaptability isinsufficient. Aiming at the lack of autonomous abilities of theconventional UAV swarm formation rotation method in terms of robustnessand adaptability, the present invention simulates migratory behavior ofmigratory birds, and designs a distributed UAV autonomous swarmformation rotation control method based on an evolutionary snowdriftgame.

In order to save energy and increase chances of survival, migratorybirds usually migrate in a tight linear formation, and there arepositional rotation cooperative behaviors. Regardless of their internalkinship, the migratory birds in the swarm have roughly the same leadingand following time, which means all individuals have the opportunity tofly in the wakes of other individuals, and are willing to sacrificetheir own interests to become the general leader. This rotation ofmigratory birds is consistent with the payoff structure of the snowdriftgame. When two individuals meet, each individual has two choices:leading (cooperation) or following (defection). If both choose tocooperate, they will both get the benefits, but at the same time bearthe cost. If both choose to defect, the gain is zero. If one individualcooperates and the other defects, the defector gains more payoff thanthe cooperator. There is a similarity in the payoff structure betweenthe UAV swarm formation rotation problem and the migratory bird generalleader rotation problem. In addition, the UAV has limited intelligenceand the environment is complex, so the individual cannot immediatelyobtain the current best strategy, which is in line with consideration ofthe limitations of individual intelligence in the evolutionary game.Individuals in the evolutionary game follow the simple rules to updatethe strategy and finally reach the evolutionarily stable strategy. Insummary, the present invention proposes a UAV autonomous swarm formationrotation control method based on a simulated migratory bird evolutionarysnowdrift game to overcome the deficiency of robustness and adaptabilityof the conventional UAV swarm formation rotation control method, whicheffectively improves the formation control level of the UAV autonomousswarm.

SUMMARY OF THE PRESENT INVENTION

The present invention provides a UAV autonomous swarm formation rotationcontrol method based on a simulated migratory bird evolutionarysnowdrift game. An object of the present invention is to provide adistributed UAV autonomous swarm formation rotation control method, soas to improve robustness and adaptability of the UAV in autonomous swarmformation rotation, thus effectively improving long-range missionexecution capability of the UAV.

Accordingly, in order to accomplish the above objects, the presentinvention provides a UAV autonomous swarm formation rotation controlmethod based on a simulated migratory bird evolutionary snowdrift gameas shown in FIG. 1, comprising steps of:

Step 1: initializing:

randomly generating initial states of N UAVs, comprising a positionP^(i), a horizontal speed V^(i), and a heading angle ψ^(i), wherein i isa UAV index, P^(i)=(X^(i), Y^(i)), X^(i) and Y^(i) are respectively thehorizontal coordinate and the vertical coordinate of the UAV i in theground coordinate system; setting the index of the leader of each UAV toN_(lead) ^(i)=0, setting current simulation time to t=0, setting asimulation counter to n=1, setting a rotation counter to Count=1, andsetting a game counter to n_(i)=0; wherein only when no UAV j satisfiesX^(j)≥X^(i) and Y^(j)≥Y_(i), the flight mode identifier Flag_(lead)^(i)(n) of UAV i is 1, the strategy S″(n) of UAV i is 1, and the reversestrategy S_(r) ^(j)(n) of UAV i is 0; otherwise, the flight modeidentifier Flag_(lead) ^(i)(n) is 0, the strategy S^(i)(n) is 0, and thereverse strategy S_(r) ^(i)(n) is 1;

Step 2: determining flight mode based on a migratory bird evolutionarysnowdrift game:

wherein if the simulation counter n>1 and the Count is less than amaximum limit Count_(max) of the rotation counter, then the rotationcounter is increased by one, and the strategy, the reverse strategy andthe flight mode identifier remain unchanged, which are Count=Count+1,S^(i)(n)=S^(i)(n−1), S_(r) ^(i)(n)=S_(r) ^(i)(n−1), Flag_(lead)^(i)(n)=Flag_(lead) ^(i)(n−1), and a Step 3 is executed;

wherein if Count=Count_(max), then the rotation counter is set to one,the neighbor strategy set S_(n) of UAV i is cleared, and the gamecounter is increased by one, which are Count=1, S_(n) ^(i)=Ø,n₁=n_(n)+1; only when no UAV j satisfies X^(j)≥X^(i) and Y^(j)≥Y^(i),the strategy S^(d)(n) is 0, the reverse strategy S_(r) ^(i)(n) is 1, thememory strategy S_(m) ^(d)(n₁) of UAV i is 0, and the flight modeidentifier Flag_(lead) ^(i)(n) is 0, then a Step 4 is executed;otherwise, a swarm consisting of the N UAVs is treated as a migratorybird flock, wherein a UAV i is a migratory bird i, the leader N_(lead)^(j) of the UAV i is the leader N_(lead) ^(j) of the migratory bird i,the strategy S^(i) (n) and the reverse strategy S_(r) ^(i) (n) of theUAV i are respectively the strategy S^(i)(n) and the reverse strategyS_(r) ^(i)(n) of the migratory bird i in an evolutionary snowdrift game;

wherein if there is a migratory bird j satisfies N_(lead) ^(j)=i, thestrategy of the migratory bird j is stored in a neighbor strategy set ofthe migratory bird i, which is S^(j) (n) ∈S_(n) ^(i), if the migratorybird i has a leader, which is N_(lead) ^(i)≠0, the strategy of themigratory bird N_(lead) ^(i) is stored in the neighbor strategy set ofthe migratory bird i, which is S^(Ni) ^(lead) (n) ∈S_(n) ^(i), realsnowdrift game payoff B^(i) of the migratory bird i is calculatedaccording to the strategy S^(i) (n) and the neighbor strategy S_(n) ^(i)of the migrato bird i:

$\begin{matrix}{B^{i} = \left\{ \begin{matrix}{{1 + r_{1}},{{{if}\mspace{14mu} {S^{i}(n)}} = 0},{1 \in S_{n}^{i}}} \\{1,{{{if}\mspace{14mu} {S^{i}(n)}} = 1},{1 \notin S_{n}^{i}}} \\{{1 - r_{2}},{{{if}\mspace{14mu} {S^{i}(n)}} = 1},{1 \in S_{n}^{i}}} \\{0,{{{if}\mspace{14mu} {S^{i}(n)}} = 0},{1 \notin S_{n}^{i}}}\end{matrix} \right.} & (1)\end{matrix}$

wherein r₁ is a benefit coefficient of a non-cooperator encounteringcooperators, r₂ is a cost coefficient of a cooperator encounteringcooperators; virtual snowdrift game payoff B_(r) ^(i) of the migratorybird i is calculated according to the reverse strategy S_(r) ^(i)(n) andthe neighbor strategy S_(n) ^(i) of the migratory bird i:

$\begin{matrix}{B_{r}^{i} = \left\{ \begin{matrix}{{1 + r_{1}},{{{if}\mspace{14mu} {S_{r}^{i}(n)}} = 0},{1 \in S_{n}^{i}}} \\{1,{{{if}\mspace{14mu} {S_{r}^{i}(n)}} = 1},{1 \notin S_{n}^{i}}} \\{{1 - r_{2}},{{{if}\mspace{14mu} {S_{r}^{i}(n)}} = 1},{1 \in S_{n}^{i}}} \\{0,{{{if}\mspace{14mu} {S_{r}^{i}(n)}} = 0},{1 \notin S_{n}^{i}}}\end{matrix} \right.} & (2)\end{matrix}$

calculating the memory strategy S_(m) ^(i)(n₁) of the migratory bird iaccording to the real snowdrift game payoff B^(i) and the virtualsnowdrift game payoff B_(r) ^(i) of the migratory bird i:

$\begin{matrix}{{S_{m}^{i}\left( n_{1} \right)} = \left\{ \begin{matrix}{{S^{i}(n)},{{{if}\mspace{14mu} B_{r}^{i}} \leq B^{i}}} \\{{S_{r}^{i}(n)},{{{if}\mspace{14mu} B_{r}^{i}} > B^{i}}}\end{matrix} \right.} & (3)\end{matrix}$

generating a selection probability p_(g) of snowdrift game strategiesbased on the memory strategy S_(m) ^(i) of the migratory bird i:

$\begin{matrix}{p_{g} = \left\{ \begin{matrix}{\frac{\sum\limits_{k = 1}^{n_{1}}\; {S_{m}^{i}(k)}}{n_{1}},{{{if}\mspace{14mu} n_{1}} < L_{m}}} \\{\frac{\sum\limits_{k = {n_{1} - L_{m} + 1}}^{n_{1}}\; {S_{m}^{i}(k)}}{L_{m}},{{{if}\mspace{14mu} n_{1}} \geq L_{m}}}\end{matrix} \right.} & (4)\end{matrix}$

wherein L_(m) is the memory length of the snowdrift game; a randomnumber rand is randomly generated, and the strategy S^(i)(n) and thereverse strategy S_(r) ^(i)(n) of the migratory bird i are generatedaccording to the selection probability p_(g) of the snowdrift gamestrategies of the migratory bird i:

$\begin{matrix}{{S^{i}(n)} = \left\{ \begin{matrix}{1,} & {{{if}\mspace{14mu} {rand}} < p_{g}} \\{0,} & {{{if}\mspace{14mu} {rand}} \geq p_{g}}\end{matrix} \right.} & (5) \\{{S_{r}^{i}(n)} = \left\{ \begin{matrix}{0,} & {{{if}\mspace{14mu} {rand}} < p_{g}} \\{1,} & {{{if}\mspace{14mu} {rand}} \geq p_{g}}\end{matrix} \right.} & (6)\end{matrix}$

updating the flight mode identifier Flag_(lead) ^(i)(n) of the UAV ibased on the strategy S^(i)(n) of the migratory bird i:

$\begin{matrix}{{{Flag}_{lead}^{i}(n)} = \left\{ \begin{matrix}{1,{{{if}\mspace{14mu} {S^{i}(n)}} = 1}} \\{0,{{{if}\mspace{14mu} {S^{i}(n)}} = 0}}\end{matrix} \right.} & (7)\end{matrix}$

Step 3: determining the leader and its position relative tocorresponding wing UAV:

wherein if the flight mode identifier Flag_(lead) ^(i)(n) is 0, the UAVi is in a wing UAV mode, which selects a nearest front UAV as theleader; if there are more than one options, the UAV i selects a UAV witha smallest index as the leader; which means only when X^(j)>X^(i) andthere is no UAV j′ satisfies X^(j)′>X^(i) and a R^(ij)′<R^(ij), orsatisfies X^(j)′>X^(i), R^(ij)′=R^(ij) and j′<j, there is N_(lead)^(i)=j, wherein R^(ij)=√{square root over((X^(i)−X^(j))²+(Y^(i)−Y^(j))²)} is the distance between the UAV i andthe UAV j; if there is no front UAV, the UAV i in the wing UAV modeselects a nearest UAV as the leader; if there are more than one options,the UAV i selects the UAV with the smallest index as the leader; whichmeans only when there is no UAV j′ satisfies X^(j)′>X^(i) and there isno UAVj″ satisfies R^(ij)″<R^(ij), or satisfies R^(ij)″=R^(ij) and j″<j,there is N_(lead) ^(i)=j, according to current positions of the UAV iand the corresponding leader N_(lead) ^(i), an expected forward positionx ^(i) and an expected lateral position y ^(i) of the correspondingleader N_(lead) ^(i) relative to the UAV i are calculated:

$\begin{matrix}{{\overset{\_}{x}}^{i} = x_{\exp}} & (8) \\{{\overset{\_}{y}}^{i} = \left\{ \begin{matrix}{y_{\exp},{{{if}\mspace{14mu} Y^{i}} \geq Y^{N_{lead}^{i}}}} \\{{- y_{\exp}},{{{if}\mspace{14mu} Y^{i}} < Y^{N_{lead}^{i}}}}\end{matrix} \right.} & (9)\end{matrix}$

wherein x_(exp) and y_(exp) are respectively the expected forwarddistance and the expected lateral distance, Y^(Ni) ^(lead) is thevertical coordinate of the leader of the UAV i in the ground coordinatesystem;

Step 4: finning UAV model:

wherein if the flight mode identifier Flag_(lead) ^(i)(n) is 1, the UAVi is in a leading UAV mode; the UAV state at next simulation time isobtained according to a leading UAV model:

$\begin{matrix}\left\{ \begin{matrix}{{{\overset{.}{X}}^{i} = {V^{i}\mspace{14mu} \cos \mspace{14mu} \psi^{i}}}\mspace{79mu}} \\{{{\overset{.}{Y}}^{i} = {V^{i}\mspace{14mu} \sin \mspace{14mu} \psi^{i}}}} \\{{\overset{.}{V}}^{i} = {{{- \frac{1}{\tau_{V}}}V^{i}} + {\frac{1}{\tau_{V}}V_{L_{C}}}}} \\{{{\overset{.}{\psi}}^{i} = {{{- \frac{1}{\tau_{\psi}}}\psi^{i}} + {\frac{1}{\tau_{\psi}}\psi_{L_{C}}}}}\mspace{11mu}}\end{matrix} \right. & (10)\end{matrix}$

wherein {dot over (X)}^(i), {dot over (Y)}^(i), {dot over (V)}^(i) and{dot over (ψ)}^(i) are respectively first-order differentials of thehorizontal coordinate, the vertical coordinate, the speed, and theheading angle of the UAV i in the ground coordinate system; τ_(V) andτ_(ψ) are respectively time constants of a Mach-hold autopilot and aheading-hold autopilot; the Mach-hold autopilot control input V_(L) _(c)of the leading UAV is V_(exp), and the heading-hold autopilot controlinput ψ_(L) _(c) of the leading UAV is ψ_(exp), V_(exp) and ψ_(exp) arerespectively the expected horizontal speed and the expected headingangle of the leading UAV; if the flight mode identifier Flag_(lead)^(i)(n) is 0, the UAV state at next simulation time is Obtainedaccording to a wing UAV model:

$\begin{matrix}\left\{ \begin{matrix}{\begin{bmatrix}X^{i} \\Y^{i}\end{bmatrix} = {\begin{bmatrix}X^{N_{lead}^{i}} \\Y^{N_{lead}^{i}}\end{bmatrix} - {\begin{bmatrix}{\cos \mspace{14mu} \psi^{i}} & {\sin \mspace{14mu} \psi^{i}} \\{\sin \mspace{14mu} \psi^{i}} & {{- \cos}\mspace{14mu} \psi^{i}}\end{bmatrix}\begin{bmatrix}x^{i} \\y^{i}\end{bmatrix}}}} \\{{{\overset{.}{x}}^{i} = {{{- \frac{{\overset{\_}{y}}^{i}}{\tau_{\psi}}}\psi^{i}} - V^{i} + V^{N_{lead}^{i}} + {\frac{{\overset{\_}{y}}^{i}}{\tau_{\psi}}\psi_{W_{C}}}}}\mspace{85mu}} \\{{{\overset{.}{y}}^{i} = {{\left( {\frac{{\overset{\_}{x}}^{i}}{\tau_{\psi}} - V^{i}} \right)\psi^{i}} + {V^{i}\psi^{i}} - {\frac{{\overset{\_}{x}}^{i}}{\tau_{\psi}}\psi_{W_{C}}}}}\mspace{104mu}} \\{{{\overset{.}{V}}^{i} = {{{- \frac{1}{\tau_{V}}}V^{i}} + {\frac{1}{\tau_{V}}V_{W_{C}}}}}\mspace{225mu}} \\{{{\overset{.}{\psi}}^{i} = {{{- \frac{1}{\tau_{\psi}}}\psi^{i}} + {\frac{1}{\tau_{\psi}}\psi_{W_{C}}}}}\mspace{236mu}}\end{matrix} \right. & (11)\end{matrix}$

wherein X^(Ni) ^(lead) and V^(Ni) ^(lead) are respectively thehorizontal coordinate and the speed of the leader of the UAV i in theground coordinate system, x^(i) and y^(i) are respectively thehorizontal coordinate and the vertical coordinate of the UAV N_(lead)^(i) in the aircraft-body coordinate system of the UAV i; the Mach-holdautopilot control input of the wing UAV is

${{V_{Wc} = {{k_{x_{p}}e_{x}} + {k_{x_{I}}{\int_{0}^{t}{e_{x}{dt}}}} + {k_{x_{D}}\frac{{de}_{x}}{dt}}}},}\ $

and the heading-hold autopilot control input of the wing UAV is

${\psi_{Wc} = {{k_{y_{p}}e_{y}} + {k_{y_{I}}{\int_{0}^{t}{e_{y}{dt}}}} + {k_{y_{D}}\frac{{de}_{y}}{dt}}}},$

(k_(x) _(p) , k_(x) _(I) , k_(x) _(D) ) and (k_(y) _(p) , k_(y) _(I) ,k_(y) _(D) ) are respectively PID (Proportional Integral Derivative)control parameters of a forward channel and a lateral channel, e_(x)=(x^(i)−x^(i))+k_(V)(V^(Ni) ^(lead) −V^(i)) is an error of the forwardchannel, e_(y)=k_(y)(y ^(i)−y^(i))+k₁₀₄ (ψ^(Ni) ^(lead) −ψ^(i)) is anerror of the lateral channel, k_(x), k_(V), k_(y) and k_(ψ) arerespectively a forward error control gain, a speed error control gain, alateral error control gain and a heading error control gain, ψ^(Ni)^(lead) is the heading angle of the leader of the UAV i; and

Step 5: determining whether to end simulation:

wherein the simulation time is t=t+ts, and is is a sampling time; if tis greater than a maximum simulation time T_(max), the simulation ends;then a UAV swarm flight trajectory, UAV swarm formations at eachrotation time, a UAV swarm horizontal speed curve and a UAV swarmheading angle curve are drawn; otherwise, the simulation returns to theStep 2.

Advantages and Effects

The present invention provides a UAV autonomous swarm formation rotationcontrol method based on a simulated migratory bird evolutionarysnowdrift game. The method is a distributed control method based on theevolutionary snowdrift game, which simulates migration of migratorybirds. The main advantages are mainly reflected in two aspects: first,the method simulates local interaction of migratory birds, so as togenerate a UAV swarm formation rotation strategy based only on recenthistory information of the UAVs and neighbors within a small range,which reduces onboard computing and communication load; second, themethod inherits environmental adaptability characteristics of themigratory birds during migration, wherein operation process does notdepend on UAV swarm formation and overall fuel configuration, which cancope with sudden failures, and has strong adaptability as well asrobustness, thus effectively improving UAV autonomous swarm formationcapability.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of UAV autonomous swarm formation rotationcontrol based on a simulated migratory bird evolutionary snowdrift game.

FIG. 2 shows a UAV swarm flight trajectory.

FIG. 3 shows a UAV swarm formation at t=3s.

FIG. 4 shows a UAV swarm formation at t=6s.

FIG. 5 shows a UAV swarm formation at t=9s.

FIG. 6 shows a UAV swarm formation at t=12s.

FIG. 7 shows a UAV swarm horizontal speed curve.

FIG. 8 shows UAV swarm heading angle curve.

ELEMENT REFERENCE

-   t—simulation time; n—simulation counter Count—rotation counter;    i—UAV index; Count_(max)—rotation counter maximum limit; Flag_(lead)    ^(i)(n)—flight mode identifier of UAV i when simulation counter is    n; N—the number of UAVs; T_(max)—maximum simulation time;    ts—sampling time.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Referring to FIGS. 1-8, effectiveness of the present invention isverified by an embodiment of a UAV autonomous swarm formation rotationcontrol. An experimental computer is configured as Intel Core i7-6700HQprocessor with 2.60 Ghz frequency, 16G memory, and MATLAB 2014a versionsoftware. The method comprises steps of:

Step 1: initializing:

randomly generating initial states of 5 UAVs, comprising positions P¹ toP⁵ of (12.5926 m, 7.1515 m), (13.1907 m, 3.2101 m), (1.4969 m, −3.1140m), (3.0873 m, 3.5804 m) and (0.5687 m, −5.9005 m) , a horizontal speedV^(i) of 42 m/s and a heading angle ψ^(i) of 0, wherein i=1,2, . . . ,5; setting the index of the leader of each UAV to N_(lead) ^(i)=0,setting current simulation time to t=0, setting a simulation counter ton=1, setting a rotation counter to Count=1, and setting a game counterto n₁=0, wherein i=1,2, . . . , 5, in the embodiment, only when no UAV jsatisfies X^(j)≥X²=13.1907 m and Y^(j)≥Y²=3.2101 m, the flight modeidentifier Flag_(lead) ²(n) is 1, the strategy S²(n) is 1, and thereverse strategy S_(r) ²(n) is 0; otherwise, the flight mode identifiersFlag_(lead) ^(i)(n) of the UAVs 1 and 3-5 are 0, the strategy S^(i)(n)is 0, and the reverse strategy S_(r) ^(i)(n) is 1, wherein i=1,3,4,5;

Step 2: determining flight mode based on a migratory bird evolutionaryto snowdrift game:

wherein if the simulation counter n>1 and the Count is less than amaximum limit Counts_(max)=300 of the rotation counter, then therotation counter is increased by one, and the strategy, the reversestrategy and the flight mode identifier remain unchanged, which areCount=Count+1, S^(i)(n)=S^(i)(n−1), S_(r) ^(i)(n)=S_(r) ^(i)(n−1),Flag_(lead) ^(i)(n)=Flag_(lead) ^(i)(n−1), and a Step 3 is executed;w/herein i=1,2, . . . , 5; if Count=300, then the rotation counter isset to one, the neighbor strategy set S_(n) ^(i) of UAV i is cleared,and the game counter is increased by one, which are Count=1, S_(n)^(i)=Ø, n₁=n₁+1; only when no UAV j satisfies X^(j)≥X^(i)andY^(j)≥Y^(i), the strategy S^(i)(n) is 0, the reverse strategy S_(i)^(d)(n) is 1, the memory strategy S_(m) ^(i)(n₁) of UAV i is 0, and theflight mode identifier Flag_(lead) ^(i)(n) is 0, then a Step 4 isexecuted; otherwise, a swarm consisting of the N UAVs is treated as amigratory bird flock, wherein a UAV i is a migratory bird i, the leaderof the N_(lead) ^(j) of the UAV i is the leader N_(lead) ^(j) of themigratory bird i, the strategy S^(s)(n) and the reverse strategy S_(r)^(j)(n) of the UAV i are respectively the strategy S^(d)(n) and thereverse strategy S_(r) ^(i)(n) of the migratory bird i in anevolutionary snowdrift game; wherein if there is a migratory bird jsatisfies N_(lead) ^(j)=i, the strategy of the migratory bird j isstored in a neighbor strategy set of the migratory bird i, which isS^(j)(n) ∈S_(n) ^(i), if the migratory bird i has a leader, which isN_(lead) ^(j)16 0, the strategy of the migratory bird N_(lead) ^(i) isstored in the neighbor strategy set of the migratory bird i, which isS^(Ni) ^(lead) (n) ∈S_(n) ^(i), real snowdrift game payoff B^(i) of themigratory bird i is calculated with an equation (1) according to thestrategy S^(i)(n) and the neighbor strategy S_(n) ^(i) of the migratorybird i; wherein a benefit r_(i) coefficient of a non-cooperatorencountering cooperators is 0.5, a cost coefficient r₂ of a cooperatorencountering cooperators is 0.2; virtual snowdrift game payoff B_(r)^(i) of the migratory bird i is calculated with an equation (2)according to the reverse strategy S_(r) ^(i)(n) and the neighborstrategy S_(n) ^(i) of the migratory bird i; the memory strategy S_(m)^(i)(n₁) of the migratory bird i is calculated with an equation (3)according to the real snowdrift game payoff B^(i) and the virtualsnowdrift game payoff B_(r) ^(i) of the migratory bird i; and aselection probability p_(g) of snowdrift game strategies is calculatedwith an equation (4) based on the memory strategy S_(m) ^(j) of themigratory bird i; wherein L_(m)=2 is the memory length of the snowdriftgame; a random number rand is randomly generated, and the strategyS^(i)(n) and the reverse strategy S_(r) ^(i)(n) of the migratory bird iare generated with equations (5) and (6) according to the selectionprobability p_(g) of the snowdrift game strategies of the migratory birdi; and the flight mode identifier Flag_(lead) ^(i)(n) of the UAV i isupdated with an equation (7) based on the strategy S^(i) (n) of themigratory bird i:

Step 3: determining the leader and its position relative tocorresponding wing UAV:

wherein if the flight mode identifier Flag_(lead) ^(i)(n) is 0, the UAVi is in a wing UAV mode, which selects a nearest front UAV as theleader; if there are more than one options, the UAV i selects a UAV witha smallest index as the leader; which means only when X^(j)>X^(i) andthere is no UAV j′ satisfies X^(j)′>X^(i) and R^(ij)′<R^(ij), orsatisfies X^(j)′>X^(i), R^(ij)′=R^(ij) and j′<j, there is N_(lead)^(i)=j, wherein R^(ij)=√{square root over((X^(i)−X^(j))²+(Y^(i)−Y^(j))²)} is the distance between the UAV i andthe UAV j; if there is no front UAV, the UAV i in the wing UAV modeselects a nearest UAV as the leader; if there are more than one optionsthe UAV i selects the UAV with the smallest index as the leader; whichmeans only when there is no UAV j′ satisfies X^(j)′>X^(i) and there isno UAV j″ satisfies R^(ij)″<R^(ij), or satisfies and R^(ij)″=R^(ij) andj″<j, there is N_(lead) ^(i)=j, according to current positions of theUAV i and the corresponding lead N_(lead) ^(i), an expected forwardposition x ^(i) and an expected lateral position y ^(i) of thecorresponding leader N_(lead) ^(i) relative to the UAV i are calculatedwith equations (8) and (9); wherein the forward expected distancex_(exp) is 3.92 m and the lateral expected distance y_(exp) is 1.54 m;

Step 4: finning UAV model:

wherein if the flight mode identifier Flag_(lead) ^(i)(n) is 1, the UAVi is in a leading UAV mode; the UAV state at a next simulation time isobtained with an equation (10) according to a leading UAV model; whereinτ_(r)=10 s and τψ=1.5 s are respectively time constants of a Mach-holdautopilot and a heading-hold autopilot: V_(exp)=42 m/s and ψ_(exp)=0 arerespectively the expected horizontal speed and the expected headingangle of the leading UAV; if the flight mode identifier Flag_(lead)^(i)(n) is 0, the UAV state at next simulation time is obtained with anequation (11) according to a wing UAV model; wherein (k_(x) _(p) , k_(x)_(I) , k_(x) _(D) )=(50,50,0.1) and (k_(y) _(p) , k_(y) _(I) , k_(y)_(D) )=(1,0.4,0) are respectively PID control parameters of a forwardchannel and a lateral channel; k_(i)=−15, k_(V)=5, k_(V)=4.5 andk_(ψ)=50 are respectively a forward error control gain, a speed errorcontrol gain, a lateral error control gain and a heading error controlgain; and

Step 5: determining whether to end simulation:

wherein the simulation time is t=t+ts, and ts=0.01 s is a sampling time;if t is greater than a maximum simulation time T_(max)=12 s , thesimulation ends; then simulation results are drawn; otherwise, thesimulation returns to the Step 2. FIG. 2 shows an overall UAV swarmflight trajectory. FIGS. 3-6 show UAV swarm formations at t=3 s, 6 s, 9s, 12 s. FIGS. 7 and 8 show an overall UAV swarm horizontal speed curveand an overall UAV swarm heading angle curve. According to UAVsimulation verification, it is proven that with the UAV autonomous swarmformation rotation control method based on the simulated migratory birdevolutionary snowdrift game of the present invention, the UAV swarm canrealize autonomous formation rotation.

What is claimed is:
 1. A UAV (Unmanned Aerial Vehicle) autonomous swarmformation rotation control method based on a simulated migratory birdevolutionary snowdrift game, comprising steps of: Step 1: initializing:randomly generating initial states of N UAVs, comprising a positionP^(i), a horizontal speed V^(i), and a heading angle ψ^(i), wherein i isa UAV index, P^(i)=(X^(i), Y^(i)), X^(i) and Y^(i) are respectively ahorizontal coordinate and a vertical coordinate of the UAV i in a groundcoordinate system; setting an index of a leader of each of the UAVs toN_(lead) ^(i)=0, setting a current simulation time to t=0, setting asimulation counter to n=1, setting a rotation counter to Count=1, andsetting a game counter to n₁=0; wherein only when no UAV j satisfiesX^(j)≥X^(i) and Y^(j)≥Y^(i), a flight mode identifier Flag_(lead)^(i)(n) of the UAV i is 1, to strategy S^(d)(n) of the UAV i is 1, and areverse strategy S_(r) ^(d)(n) of the UAV i is 0; otherwise, the flightmode identifier Flag_(lead) ^(i)(n) is 0, the strategy S^(d)(n) is 0,and the reverse strategy S_(r) ^(i)(n) is 1; Step 2: determining aflight mode based on a migratory bird evolutionary snowdrift game:wherein if the simulation counter n>1 and the Count is less than amaximum limit Count_(max) of the rotation counter, then the rotationcounter is increased by one, and the strategy, the reverse strategy andthe flight mode identifier remain unchanged, which are Count=Count+1,S^(i)(n)=S^(i)(n−1), S_(r) ^(i)(n)=S_(r) ^(i)(n−1), Flag_(lead)^(i)(n)=Flag_(lead) ^(i)(n−1), and a Step 3 is executed; wherein ifCount=Count_(max), then the rotation counter is set to one, a neighborstrategy set S_(n) ^(i) of the UAV i is cleared, and the game counter isincreased by one, which are Count=1, S_(n) ^(i)=Ø, n₁=n₁+1; only when noUAV j satisfies X^(j)≥X^(i) and Y^(j)≥Y^(i), the strategy S^(i)(n) is 0,the reverse strategy S_(r) ^(i)(n) is 1, a memory strategy S_(m)^(i)(n₁) of the UAV i is 0, and the flight mode identifier Flag_(lead)^(i)(n) is 0, then a Step 4 is executed; otherwise, a swarm consistingof the N UAVs is treated as a migratory bird flock, wherein a UAV i is amigratory bird i , a leader N_(lead) ^(j) of the UAV i is a leaderN_(lead) ^(i) of the migratory bird i , the strategy S^(i)(n) and thereverse strategy S_(r) ^(i)(n) of the UAV i are respectively a strategyS^(i)(n) and a reverse strategy S_(r) ^(i)(n) of the migratory bird i inan evolutionary snowdrift game; wherein if there is a migratory bird jsatisfies N_(lead) ^(j)=i, the strategy of a migratory bird j is storedin a neighbor strategy set of the migratory bird i, which is S^(j)(n)∈S_(n) ^(i), if the migratory bird i has a leader, which is N_(lead)^(i)≠0, the strategy of the migratory bird N_(lead) ^(i) is stored inthe neighbor strategy set of the migratory bird i, which is S_(lead)^(N)(n) ∈S_(n) ^(i), a real snowdrift game payoff B^(i) of the migratorybird i is calculated according to the strategy S^(i)(n) and a neighborstrategy S_(n) ^(i) of the migratory bird i: $\begin{matrix}{B^{i} = \left\{ \begin{matrix}{{1 + r_{1}},{{{if}\mspace{14mu} {S^{i}(n)}} = 0},{1 \in S_{n}^{i}}} \\{1,{{{if}\mspace{14mu} {S^{i}(n)}} = 1},{1 \notin S_{n}^{i}}} \\{{1 - r_{2}},{{{if}\mspace{14mu} {S^{i}(n)}} = 1},{1 \in S_{n}^{i}}} \\{0,{{{if}\mspace{14mu} {S^{i}(n)}} = 0},{1 \notin S_{n}^{i}}}\end{matrix} \right.} & (1)\end{matrix}$ wherein r₁ is a benefit coefficient of a non-cooperatorencountering cooperators, r₂ is a cost coefficient of a cooperatorencountering cooperators; virtual snowdrift game payoff of the migratorybird i is calculated according to the reverse strategy S_(r) ^(i)(n) andthe neighbor strategy S_(n) ^(i) of the migratory bird i:$\begin{matrix}{B_{r}^{i} = \left\{ \begin{matrix}{{1 + r_{1}},{{{if}\mspace{14mu} {S_{r}^{i}(n)}} = 0},{1 \in S_{n}^{i}}} \\{1,{{{if}\mspace{14mu} {S_{r}^{i}(n)}} = 1},{1 \notin S_{n}^{i}}} \\{{1 - r_{2}},{{{if}\mspace{14mu} {S_{r}^{i}(n)}} = 1},{1 \in S_{n}^{i}}} \\{0,{{{if}\mspace{14mu} {S_{r}^{i}(n)}} = 0},{1 \notin S_{n}^{i}}}\end{matrix} \right.} & (2)\end{matrix}$ calculating the memory strategy S_(m) ^(i)(n₁) of themigratory bird i according to the real snowdrift game payoff B^(i) andthe virtual snowdrift game payoff B_(r) ^(i) of the migratory bird i:$\begin{matrix}{{S_{m}^{i}\left( n_{1} \right)} = \left\{ \begin{matrix}{{S^{i}(n)},{{{if}\mspace{14mu} B_{r}^{i}} \leq B^{i}}} \\{{S_{r}^{i}(n)},{{{if}\mspace{14mu} B_{r}^{i}} > B^{i}}}\end{matrix} \right.} & (3)\end{matrix}$ generating a selection probability p_(g) of snowdrift gamestrategies based on the memory strategy S_(m) ^(i), of the migratorybird i: $\begin{matrix}{p_{g} = \left\{ \begin{matrix}{\frac{\sum\limits_{k = 1}^{n_{1}}\; {S_{m}^{i}(k)}}{n_{1}},{{{if}\mspace{14mu} n_{1}} < L_{m}}} \\{\frac{\sum\limits_{k = {n_{1} - L_{m} + 1}}^{n_{1}}\; {S_{m}^{i}(k)}}{L_{m}},{{{if}\mspace{14mu} n_{1}} \geq L_{m}}}\end{matrix} \right.} & (4)\end{matrix}$ wherein L_(m) is a memory length of the snowdrift game; arandom number rand is randomly generated, and the strategy S^(d) (n) andthe reverse strategy S_(r) ^(i)(n) of the migratory bird i are generatedaccording to the selection probability p_(g) of the snowdrift gamestrategies of the migratory bird i: $\begin{matrix}{{S^{i}(n)} = \left\{ \begin{matrix}{1,} & {{{if}\mspace{14mu} {rand}} < p_{g}} \\{0,} & {{{if}\mspace{14mu} {rand}} \geq p_{g}}\end{matrix} \right.} & (5) \\{{S_{r}^{i}(n)} = \left\{ \begin{matrix}{0,} & {{{if}\mspace{14mu} {rand}} < p_{g}} \\{1,} & {{{if}\mspace{14mu} {rand}} \geq p_{g}}\end{matrix} \right.} & (6)\end{matrix}$ updating the flight mode identifier Flag_(lead) ^(i)(n) ofthe UAV i based on the strategy S^(i)(n) of the migratory bird i:$\begin{matrix}{{{Flag}_{lead}^{i}(n)} = \left\{ \begin{matrix}{1,{{{if}\mspace{14mu} {S^{i}(n)}} = 1}} \\{0,{{{if}\mspace{14mu} {S^{i}(n)}} = 0}}\end{matrix} \right.} & (7)\end{matrix}$ Step 3: determining the leader and a position thereofrelative to a corresponding wing UAV: wherein if the flight modeidentifier Flag_(lead) ^(i)(n) is 0, the UAV i is in a wing UAV mode,which selects a nearest front UAV as the leader; if there are more thanone options, the UAV i selects a UAV with a smallest index as theleader; which means only when X^(j)>X^(i) and there is no UAV j′satisfies X^(j)′>X^(i) and R^(ij)′<R^(ij), or satisfies X^(j)>X^(j),R^(ij)′=R^(ij) and j′<j, there is N_(lead) ^(i)=j, whereinR^(ij)=√{square root over ((X^(i)−X^(j))²+(Y^(i)−Y^(j))²)} is a distancebetween the UAV i and the UAV j; if there is no front UAV, the UAV i inthe wing UAV mode selects a nearest UAV as the leader; if there are morethan one options, the UAV selects the UAV with the smallest index as theleader; which means only when there is no UAV j′ satisfies X^(j)′>X^(j)and there is no UAV j″ satisfies R^(ij)″<R^(ij), or satisifiesR^(ij)″=R^(ij) and j″<j, there is N_(lead) ^(i)=j, according to currentpositions of the UAV i and a corresponding leader N_(lead) ^(i), anexpected forward position x ^(i) and an expected lateral position y ^(i)of the corresponding leader N_(lead) ^(i) relative to the UAV i arecalculated: $\begin{matrix}{{\overset{\_}{x}}^{i} = x_{\exp}} & (8) \\{{\overset{\_}{y}}^{i} = \left\{ \begin{matrix}{y_{\exp},{{{if}\mspace{14mu} Y^{i}} \geq Y^{N_{lead}^{i}}}} \\{{- y_{\exp}},{{{if}\mspace{14mu} Y^{i}} < Y^{N_{lead}^{i}}}}\end{matrix} \right.} & (9)\end{matrix}$ wherein x_(exp) and y_(exp) are respectively an expectedforward distance and an expected lateral distance, Y^(Ni) ^(lead) is avertical coordinate of the leader of the UAV i in the ground coordinatesystem; Step 4: running a UAV model: wherein if the flight modeidentifier Flag_(lead) ^(i)(n) is 1, the UAV i is in a leading UAV mode;a UAV state at a next simulation time is obtained according to theleading UAV model: $\begin{matrix}\left\{ \begin{matrix}{{{\overset{.}{X}}^{i} = {V^{i}\mspace{14mu} \cos \mspace{14mu} \psi^{i}}}\mspace{79mu}} \\{{{\overset{.}{Y}}^{i} = {V^{i}\mspace{14mu} \sin \mspace{14mu} \psi^{i}}}} \\{{\overset{.}{V}}^{i} = {{{- \frac{1}{\tau_{V}}}V^{i}} + {\frac{1}{\tau_{V}}V_{L_{C}}}}} \\{{{\overset{.}{\psi}}^{i} = {{{- \frac{1}{\tau_{\psi}}}\psi^{i}} + {\frac{1}{\tau_{\psi}}\psi_{L_{C}}}}}\mspace{11mu}}\end{matrix} \right. & (10)\end{matrix}$ wherein {dot over (X)}^(i), {dot over (Y)}^(i), {dot over(V)}^(i) and {dot over (ψ)}^(i) are respectively first-orderdifferentials of the horizontal coordinate, the vertical coordinate, thespeed, and the heading angle of the UAV i in the ground coordinatesystem; τ_(V) and τ_(ψ) are respectively time constants of a Mach-holdautopilot and a heading-hold autopilot; the Mach-hold autopilot controlinput V_(L), of the leading UAV is V_(exp), and a heading-hold autopilotcontrol input ψ_(L) _(c) of the leading UAV is ψ_(exp), V_(exp) andψ_(exp) are respectively an expected horizontal speed and an expectedheading angle of the leading UAV; if the flight mode identifierFlag_(lead) ^(i)(n) is 0, the UAV state at next simulation time isobtained according to a wing UAV model: $\begin{matrix}\left\{ \begin{matrix}{\begin{bmatrix}X^{i} \\Y^{i}\end{bmatrix} = {\begin{bmatrix}X^{N_{lead}^{i}} \\Y^{N_{lead}^{i}}\end{bmatrix} - {\begin{bmatrix}{\cos \mspace{14mu} \psi^{i}} & {\sin \mspace{14mu} \psi^{i}} \\{\sin \mspace{14mu} \psi^{i}} & {{- \cos}\mspace{14mu} \psi^{i}}\end{bmatrix}\begin{bmatrix}x^{i} \\y^{i}\end{bmatrix}}}} \\{{{\overset{.}{x}}^{i} = {{{- \frac{{\overset{\_}{y}}^{i}}{\tau_{\psi}}}\psi^{i}} - V^{i} + V^{N_{lead}^{i}} + {\frac{{\overset{\_}{y}}^{i}}{\tau_{\psi}}\psi_{W_{C}}}}}\mspace{85mu}} \\{{{\overset{.}{y}}^{i} = {{\left( {\frac{{\overset{\_}{x}}^{i}}{\tau_{\psi}} - V^{i}} \right)\psi^{i}} + {V^{i}\psi^{i}} - {\frac{{\overset{\_}{x}}^{i}}{\tau_{\psi}}\psi_{W_{C}}}}}\mspace{104mu}} \\{{{\overset{.}{V}}^{i} = {{{- \frac{1}{\tau_{V}}}V^{i}} + {\frac{1}{\tau_{V}}V_{W_{C}}}}}\mspace{225mu}} \\{{{\overset{.}{\psi}}^{i} = {{{- \frac{1}{\tau_{\psi}}}\psi^{i}} + {\frac{1}{\tau_{\psi}}\psi_{W_{C}}}}}\mspace{236mu}}\end{matrix} \right. & (11)\end{matrix}$ wherein X^(Ni) ^(lead) and V^(Ni) ^(lead) are respectivelya horizontal coordinate and a speed of the leader of the UAV i in theground coordinate system, x^(i) and y^(i) are respectively a horizontalcoordinate and a vertical coordinate of the UAV N_(lead) ^(i) in anaircraft-body coordinate system of the UAV i ; the Mach-hold autopilotcontrol input of the wing UAV is${{V_{Wc} = {{k_{x_{p}}e_{x}} + {k_{x_{I}}{\int_{0}^{t}{e_{x}{dt}}}} + {k_{x_{D}}\frac{{de}_{x}}{dt}}}},}\ $and a heading-hold autopilot control input of the wing UAV is${\psi_{Wc} = {{k_{y_{p}}e_{y}} + {k_{y_{I}}{\int_{0}^{t}{e_{y}{dt}}}} + {k_{y_{D}}\frac{{de}_{y}}{dt}}}},$(k_(x) _(p) , k_(x) _(I) , k_(x) _(D) ) and (k_(y) _(p) , k_(y) _(I) ,k_(y) _(D) ) are respectively PID (Proportional Integral Derivative)control parameters of a forward channel and a lateral channel,e_(x)=k_(x)(x ^(i)−x^(i))+k_(V)(V^(Ni) ^(lead) −V^(i)) is an error ofthe forward channel, e_(y)=k_(y)(y ^(i)−y^(i))+k₁₀₄ (ψ^(Ni) ^(lead)−ψ^(i)) is an error of the lateral channel, k_(x), k_(V), k_(y) andk_(ψ) are respectively a forward error control gain, a speed errorcontrol gain, a lateral error control gain and a heading error controlgain, ψ^(Ki) ^(lead) is the heading angle of the leader of the UAV i;and Step 5: determining whether to end simulation: wherein a simulationtime is t=t+ts, and is is a sampling time; if t is greater than amaximum simulation time T_(max), the simulation ends; then a UAV swarmflight trajectory, UAV swarm formations at each rotation time, a UAVswarm horizontal speed curve and a UAV swarm heading angle curve aredrawn; otherwise, the simulation returns to the Step 2.